In every case where you say "master die" you actually mean either master hub or working hub.
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Look at it this way, the master die is set correctly at three o’clock (on a clock face). Then, there is a very slight, almost imperceptible, move to the right or left
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This sounds more like off-set hub doubling than pivoted hub doubling. I would suggest replacing "move to the left or right" with "rotated either clockwise or counterclockwise around that point."
And the pivot point does not have to be on the rim, it can actually be located at any spot on the die face. For this reason, even though rotated hub doubling is given a separate class number it is really just a special case of pivoted hub doubling where the pivot point is in the exact center of the die face.